PART III: APPLICATION 5. a and b have magnitudes of 5 and 6, respectively. The angle between them is 30-. a) Represent the vectors using a parallelogram. b) Draw and label a + b and a b , then calculate the magnitudes of both.

Q: 5. The denominator of a fraction is four less than the numerator. If the denominator is doubled and…

A:

Q: www 1D syppose that a sequence CanZ is definel by the envations az =2 cand anti = following is true…

A: Clearly,

Q: + 3x² 4)dx

A: Given query is to find the value of the integral.

Q: 2. C sin $ 2wcos° 2wcw 3. If f(x) = Vi19+r² dt , find f'(3).

A:

Q: V = f(x, y) = x²y ,x(t) = 2.

A:

Q: 2) (-2)77"= 5h hzo

A:

Q: Solve the problem. A conitant force F 10+ 30J. moves an object from the point P= (6, 4) to the point…

A: Given  F=16i+30j             P=(6,4) & Q=(3,18) To find work-done:

Q: 54. Find numbers a, b and c such that x = 1 + at y = 2+ bt is perpendicular to 2x + y - 3z = 1 z 3+…

A:

Q: Find the polar equution for the cartesian curve r=8 sin o Cos o r=8 sec e tan E r=8 sine tan E r=8…

A:

Q: x²+x dx x2+1

A:

Q: dx (r-1)%

A:

Q: А В C D E F This is a graph of f'(x), the derivative of f(x). At which of the marked values is: f(x)…

A:

Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: We have to find integral

Q: Find the third degree Taylor polynomial centered at 2 for the function f(x)=e²* + 3.x .

A:

Q: Find the unit tangent vector to the curve at the specified value of the paramet r(t) = 4 cos(t)i + 4…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | cos(7/x29) dx

A:

Q: Monthly sales of a particular personal computer are expected to decline at the following rate of…

A: calculation of above requirement are as follows

Q: What u-substitution should be made in order to evaluate the following integral? dx (6x² + 4)* u =

A:

Q: Find the required limit or indicate that it does not exist. lim o+ (in (t6), 12 in t O 6i O Does not…

A: We have to find out

Q: 26) (a) Sketch the region between the given functions (curves): y= 2x and y=x (b) Calculate the area…

A: Given: Curves: y=2x, y=x2

Q: Below is a graph of f' (x), the derivative of f(x). A B D E F When is: f(x) greatest? f(x) least? f…

A:

Q: Question 5 3 Consider the function f(x) = Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A:

Q: 4 sin 3xcar" 3xdx

A:

Q: Y – C(Y)-I(i)–G, =0 kY +L(i)– M20 =0 %3D

A: answer is in next step

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

A: Here , we have given an integral and we have to integrate over a rectangle whose vertices are given…

Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

A:

Q: dr 2 Vr*+3

A:

Q: If 39 | f(z)dz = 7 - 89 and - 39 g(x)dx = 25 89 and 39 | h(x)dæ = 32 89 what does the following…

A:

Q: A) S sin edo b)S sec edo )Side Ssec?eddo E)S cos ede

A: We have to find the integral

Q: .1//7 7 arccos x x² dx V1- x 1 –

A:

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, y, - 2z) across the…

A:

Q: 2) 2x2 csck) dy d X M) y'= Xe'Vx-2

A:

Q: Solve the problem. dV The growth rate of a certain stock is modeled by = k(25 - V), V = 20 when t=…

A:

Q: ind r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). r(t) 클리 - 5j + 6 (a) r'(t) (b) r"(t) (c) r'(t) ·…

A:

Q: uestion 19 Describe the largest set S on which it is correct to say that f is continuous. f(x, y, z)…

A:

Q: 3. The tens digit of a two-digit number is thrice the units digit and their difference is 6. Find…

A: Solution: Let unit digit =x  and tenth digit=y  Now According to question: y=3x ---------(I) y-x=6…

Q: Solve the following differential equations of cos (y) y'+sin(y) = x

A:

Q: Find the indefinite integral by using the substitution x = 3 sec(0). (Use C for the constant of…

A:

Q: dx V1-e2x

A: A detailed solution is given below.

Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: Write an iterated integral for J dA over the region R described to the right using R a. vertical…

A:

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Solution: C′(x)=3x2 −5x​; C(0)=2,000

Q: Suppose that f (x) is a function such that lim f(r) and lim f (r) both exist. Does this mean lim…

A:

Q: The eccentricities and foci of a hyperbola centered at the origin of the xy-plane are shown below.…

A: The eccentricity of the hyperbola centered at the origin of the xy-plane, e = 2 The coordinates of…

Q: -2 12) Find the sum of the Series 2".30" A C) D) 2 E) 9

A: Let    I= ∑n=1∞2n3-n-2Rewriting 2n3-n-2=2n3-n3-2                                  =2n3n×132…

Q: Find T(t) and N(t) at the given poi: x = e cos t, y=e' sin t, z = %3D %3D T(0) = N(0) = %3D

A:

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: ∫tndt = t(n+1)/(n+1) +C ,C is a constant and for any real number n. d/dt (tn)= nt(n-1) , for any…

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

A:

Q: Evaluate the integral using the following values. 8 8. x3 dx = 960, x dx = 24, dx = 4 x3 dx

A:

Q: Find ify= xln(4x +1)

A: